Document 13211879

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Math 479 Dg 42
:
-
The
reason
So
for
hug
multiple models far the hyperbolic plane
new
'
u
gas
geodesic
of
He
desire
fr simple
geodesics
.
:
.
Fi t2u
'
'
Hit
'
Recall the
IH
geodesics in
consider
bk
Hyf )
is
'
v
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Hit
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Ri
=o
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if
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to
x
(
then
,
then
we
C
,
write
on
A
Bt
e
datx
)
give sohfny
'
x
y
case
.
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,
of
,
the
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thy
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4
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'
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y
'
.
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it
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souk
Sine th
data
3
a
-
=
separable
ty
.
,
ldiffakl qn
let C
or
in
,
nice
fan
,
lift #yaa÷z
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,
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xtcz
xtty
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.
=
=
pot integrate
wean
Est
axtb
that't at
D
.
,
xtDz
tie
taolyaatxt
to get
-1
After
naipbth
this
,
j
is
×
so
tht there gods
see
we
Dikes
Kw pts :
for
oft
gn
c
I
thtae DIP Q )
,
,
So
,
for
Of
first
exnk
Cone
we
.
all
of
an
,
see
an
ftz )
,
tht
th
se
=
}÷
the
Of
cone
,
&
segment
hkich
hs to
<
.
if
}
to
,
=
o
o
a
the
Them
3
"
.
gods
.
Q =L
fine
,
x,
at
,
angles
in IH
funny
we think
f
as
x
mps to
not be aide
hopes
an
ah the
are
of
a
atz
=
.
Hw then
2
gin
is
by
so
,
as
a
2
a
to
=
=
c2
In
(K)
.
⇐>
DIP QI
Ihl %) I
=
,
.
.
D
in
is
.
so
X
-
Bonetti
since
,
9
mjtnp
gods
it not up Lynn lied ) able
x
-
axis
ktnutiy
f
popudiahf
to the
axis
edpowb
and
.
b
=
ktrscdy the
f
since
'd
a
a
its utml
so
semicircles
>
b)
the gods
are
&
.
d IP, Q )
th
,
'
ace
,
Presho afbs
f
-
putted f adgth
be
ltd
alt )
b
int f suds
soneky
b)
x,
x
412=6 do
poses
kind
,
=/IHP
Since the gods is in IH
as
tx
seeds
che
=
QH
&
)
(
I
=
a
the
on
)
it
Rt the
.
centered
semicircles
are
p= ( × ,
a
,
btayt
=
,
is
ggpn
A)
off +42
-
wit
the aide
f ifmite
radio )
cirle (the
wit able
the
are
.
&
are
since
"
'
Y
to
geodes is
areas
to
tented )
f
sends
cnle
body at int nig
pepediuhf
antipodal
:
"
of
.
circle arcs
ones
to
D) , then
.
ya
at
a
straight the
.
circle
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